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Effects of Hawking evaporation on PBH distributions

by Markus R. Mosbech, Zachary S. C. Picker

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Submission summary

As Contributors: Markus Mosbech · Zachary Picker
Preprint link: scipost_202203_00022v1
Date submitted: 2022-03-17 05:08
Submitted by: Mosbech, Markus
Submitted to: SciPost Physics
Academic field: Physics
  • Gravitation, Cosmology and Astroparticle Physics


Primordial black holes (PBHs) lose mass by Hawking evaporation. For sufficiently small PBHs, they may lose a large portion of their formation mass by today, or even evaporate completely if they form with mass $M<M_{\mathrm{crit}}\sim5\times10^{14}~\mathrm{g}$. We investigate the effect of this mass loss on extended PBH distributions, showing that the shape of the distribution is significantly changed between formation and today. We reconsider the $\gamma$-ray constraints on PBH dark matter in the Milky Way center with a correctly `evolved' lognormal distribution, and derive a semi-analytic time-dependent distribution which can be used to accurately project monochromatic constraints to extended distribution constraints. We also derive the rate of black hole explosions in the Milky Way per year, finding that although there is a significant number, it is extremely unlikely to find one close enough to Earth to observe. Along with a more careful argument for why monochromatic PBH distributions are unlikely to source an exploding PBH population today, we (unfortunately) conclude that we are unlikely to witness any PBH explosions.

Current status:
Has been resubmitted

Reports on this Submission

Report 2 by Kaz Kohri on 2022-7-8 (Invited Report)


Basically, I also agree with the main points raised by the first referee (Anonymous Report 1 ). The concrete calculations and computations done in this article with the lognormal distribution of PBHs warrant publication in SciPost Physics.

However, modifications of the distribution for evaporating PBHs with near critical masses (O(1.e15) gram) themselves have been known well, and constrained on PBHs obtained by gamma-ray observations towards the Galactic center have been also studied in details, e.g., in Carr et al, 2016, arXiv1604.05349 for both broad and monochromatic distributions although the broad distributions assumed in arXiv1604.05349 were not the lognormal one.

In addition, it is also known that observational non-detections of the explosion should not severaly constrain abundances of the PBHs with near critical masses compared with the ones obtained by either isotropic diffuse gamma-ray backgroud shown in Ref.[8] or galactic gamma-rays. However, it is valualbe to show this thing explicitely as was don in this paper.

  • validity: high
  • significance: good
  • originality: ok
  • clarity: good
  • formatting: good
  • grammar: reasonable

Anonymous Report 1 on 2022-4-1 (Invited Report)


See below


See below


This manuscript reports several calculations relating to evaporating PBHs. The calculation of the gamma-ray constraint on the PBH abundance, correctly taking into account the evolution of the PBH mass, is interesting and warrants publication in SciPost Physics. However the presentation of the manuscript requires improvement.

Requested changes

Major comments:

i) The structure of the manuscript requires improvement. Material should be presented clearly and concisely, in a logical order. For instance figure 2 appears before the lognormal mass function and the evolution of the PBH mass have been introduced, see also ii) below.

ii) The fact that the dark matter could be in PBHs which today have M<M_crit, and that the present day mass of those PBHs depends sensitively on the initial PBH mass, is a point worth making. However it doesn't warrant an entire section. It could be done in a short paragraph. I don't think Fig. 1 is sufficiently informative to be worth including; the point is more clearly made by the numerical example in the text. The time dependence of the PBH mass plays a crucial role in this point, so this discussion needs to appear after Eqs. (7) and (8).

iii) The lognormal mass function requires more justification/explanation. Specifically it should be made clear that
a) it's a fit to the PBH mass functions formed by (for instance) the collapse of density perturbations produced by some inflation models,
b) the low mass tail of the initial PBH mass function deviates significantly from a lognormal, see Gow, Byrnes and Hall (
The later point may have a non-negligible effect on the constraints.

iv) The figure captions need rewriting. Figure captions should comprehensively, but concisely, describe what is shown in the figure. Discussion of implications should take place in the main body of the paper. For instance, in Fig. 4, what exactly do the crosses, dots, solid and dotted lines denote? The caption for Fig. 5 is far too long.

v) Section 5 needs to be put into context. What previous work has been done on the detectability of BH explosions? How do your calculations and conclusions differ?

vi) The manuscript should be proofread carefully, to make sure that the English is clear and precise. There are various unclear and/or unscientific statements. e.g. "which species are possible to emit", "does not make for a nice analytic solution", "the evolution itself is evolving", "there is a lot of possibility when the entire particle spectrum is produced" "convert... a plot... ...which we plot..."

Minor comments:

i) Ref. [28] should also be cited at the end of the sentence "Typically these constraints... ... growing interest in studying extended mass distributions [10-14]"

ii) MacGibbon, Carr and Page (, should be cited for the numerical value of M_crit.

iii) The original source of Eq.(7) should be cited in the text preceeding it.

iv) g is missing after 10^{18} at the bottom of page 6.

v) If I recall correctly, the M^2 scaling of the PBH mass function at low masses has previously been found, possibly by Carr and collaborators. This should be checked, and a citation added, if this is the case.

vi) Journal details are missing from some references.

  • validity: good
  • significance: ok
  • originality: ok
  • clarity: low
  • formatting: reasonable
  • grammar: acceptable

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Anonymous on 2022-07-08  [id 2644]

Basically, I also agree with the main points raised by the first referee (Anonymous Report 1 ). The concrete calculations and computations done in this article with the lognormal distribution of PBHs warrant publication in SciPost Physics.